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Mirrors > Home > ILE Home > Th. List > elcncf1di | Unicode version |
Description: Membership in the set of
continuous complex functions from ![]() ![]() |
Ref | Expression |
---|---|
elcncf1d.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
elcncf1d.2 |
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elcncf1d.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
elcncf1di |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elcncf1d.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | elcncf1d.2 |
. . . . . 6
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3 | 2 | imp 124 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | an32 562 |
. . . . . . . . 9
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5 | 4 | anbi2i 457 |
. . . . . . . 8
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6 | anass 401 |
. . . . . . . 8
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7 | 5, 6 | bitr4i 187 |
. . . . . . 7
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8 | elcncf1d.3 |
. . . . . . . 8
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9 | 8 | imp 124 |
. . . . . . 7
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10 | 7, 9 | sylbir 135 |
. . . . . 6
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11 | 10 | ralrimiva 2550 |
. . . . 5
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12 | breq2 4006 |
. . . . . 6
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13 | 12 | rspceaimv 2849 |
. . . . 5
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14 | 3, 11, 13 | syl2anc 411 |
. . . 4
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15 | 14 | ralrimivva 2559 |
. . 3
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16 | 1, 15 | jca 306 |
. 2
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17 | elcncf 13922 |
. 2
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18 | 16, 17 | syl5ibrcom 157 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 ax-un 4432 ax-setind 4535 ax-cnex 7898 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-iota 5176 df-fun 5216 df-fn 5217 df-f 5218 df-fv 5222 df-ov 5874 df-oprab 5875 df-mpo 5876 df-map 6646 df-cncf 13920 |
This theorem is referenced by: elcncf1ii 13929 cncfmptc 13944 cncfmptid 13945 addccncf 13948 negcncf 13950 |
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